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Differentiates a circuit using Central Differencing.

Inherits From: LinearCombination

    error_order=2, grid_spacing=0.001

Central differencing computes a derivative at point x using an equal number of points before and after x. A closed form for the coefficients of this derivative for an arbitrary positive error order is used here, which is described in the following article: https://www.sciencedirect.com/science/article/pii/S0377042799000886.

my_op = tfq.get_expectation_op() 
linear_differentiator = tfq.differentiators.CentralDifference(2, 0.01) 
# Get an expectation op, with this differentiator attached. 
op = linear_differentiator.generate_differentiable_op( 
qubit = cirq.GridQubit(0, 0) 
circuit = tfq.convert_to_tensor([ 
    cirq.Circuit(cirq.X(qubit) ** sympy.Symbol('alpha')) 
psums = tfq.convert_to_tensor([[cirq.Z(qubit)]]) 
symbol_values_array = np.array([[0.123]], dtype=np.float32) 
# Calculate tfq gradient. 
symbol_values_tensor = tf.convert_to_tensor(symbol_values_array) 
with tf.GradientTape() as g: 
    expectations = op(circuit, ['alpha'], symbol_values_tensor, psums) 
# Gradient would be: -50 * f(x + 0.02) +  200 * f(x + 0.01) - 150 * f(x) 
grads = g.gradient(expectations, symbol_values_tensor) 
tf.Tensor([[-1.1837807]], shape=(1, 1), dtype=float32) 


  • error_order: A positive, even int specifying the error order of this differentiator. This corresponds to the smallest power of grid_spacing remaining in the series that was truncated to generate this finite differencing expression.
  • grid_spacing: A positive float specifying how large of a grid to use in calculating this finite difference.



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    programs, symbol_names, symbol_values, pauli_sums, forward_pass_vals, grad


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    programs, symbol_names, symbol_values, pauli_sums, num_samples,
    forward_pass_vals, grad


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Generate a differentiable op by attaching self to an op.

This function returns a tf.function that passes values through to forward_op during the forward pass and this differentiator (self) to backpropagate through the op during the backward pass. If sampled_op is provided the differentiators differentiate_sampled method will be invoked (which requires sampled_op to be a sample based expectation op with num_samples input tensor). If analytic_op is provided the differentiators differentiate_analytic method will be invoked (which requires analytic_op to be an analytic based expectation op that does NOT have num_samples as an input). If both sampled_op and analytic_op are provided an exception will be raised.


This generate_differentiable_op() can be called only ONCE because of the one differentiator per op policy. You need to call refresh() to reuse this differentiator with another op.


  • sampled_op: A callable op that you want to make differentiable using this differentiator's differentiate_sampled method.
  • analytic_op: A callable op that you want to make differentiable using this differentiators differentiate_analytic method.


A callable op that who's gradients are now registered to be a call to this differentiators differentiate_* function.


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Refresh this differentiator in order to use it with other ops.